Routes to chaos and bistability in the Rypdal model with a parametric disturbance

Abstract

In this work, we propose a parametric perturbation in the plasma production rate of the Rypdal model. This low-dimensional Lorenz-like system is derived from a two-field model for transport in Helimak magnetically confined plasmas. We analyze the stability of the equilibrium points and study the emergence of chaos in the disturbed system. As a perturbation result, the attractor structure is modified, and shrimp-shaped domains occur in the parameter plane, where there are periodic spirals immersed in the chaotic region, both behaviors characterized by the largest Lyapunov exponent. Along these periodic domains, we identify the bistability of attractors, period-doubling cascades, and a route to chaos via bifurcations and collisions of periodic orbits. By the isospikes per period, we schematize the hierarchical organization of periodic attractors into the shrimp spirals.